The Normal Impact of a Rod-Mass System on a Viscoelastic Layered Half Space

[+] Author and Article Information
H. A. Downey

IBM Corporation, Charlotte, NC 28257

D. B. Bogy

University of California, Berkeley, CA 94720

J. Appl. Mech 55(4), 879-886 (Dec 01, 1988) (8 pages) doi:10.1115/1.3173736 History: Received November 06, 1987; Revised April 12, 1988; Online July 21, 2009


A rod with a lumped mass attached to its trailing end travels axially with a uniform velocity and strikes an elastic half space that is covered with an adhering viscoelastic layer. The problem is reduced to integral equations for the average contact stress and the displacement of the rod tip into the contact surface. The kernels of these integral equations are composed of temporal Green’s functions for the rod and the layered half space, which represent the response of each to an impulsive uniform normal traction. The Green’s function for the rod is obtained in closed form, while that for the layered half space is obtained through a numerical Laplace transform inversion. The integral equations are solved numerically with a second-order stable scheme. Solutions are computed for a wide variety of materials and configurations, providing the stress and displacement history, as well as the stress-displacement response. The results show the effects of changes in rod material and length, lumped mass, layer material, substrate material, and viscoelastic material parameters.

Copyright © 1988 by ASME
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